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JEE (Main) Mathematics - Functions

JEE (Main) Mathematics - Functions (Questions 46 to 60)

46. If \( f(x) = x^2 \), then the function is:
a) One-to-one
b) Onto
c) Many-to-one
d) One-to-one and onto
Answer: c) Many-to-one
47. Which of the following functions is not one-to-one?
a) \( f(x) = x + 2 \)
b) \( f(x) = 2x \)
c) \( f(x) = x^2 \)
d) \( f(x) = 3x + 1 \)
Answer: c) \( f(x) = x^2 \)
48. If \( f \) and \( g \) are both one-to-one functions, then \( g \circ f \) is:
a) One-to-one
b) Onto
c) Neither one-to-one nor onto
d) Both one-to-one and onto
Answer: a) One-to-one
49. A function \( f: A \to B \) is said to be onto if:
a) Every element of \( B \) has a pre-image in \( A \)
b) Every element of \( A \) is mapped to a unique element of \( B \)
c) The image of \( A \) covers all elements of \( B \)
d) Both a) and c)
Answer: d) Both a) and c)
50. The composition of functions \( f: A \to B \) and \( g: B \to C \) is:
a) \( g \circ f = g(f(x)) \)
b) \( g \circ f = f(g(x)) \)
c) \( f \circ g = g(f(x)) \)
d) None of the above
Answer: a) \( g \circ f = g(f(x)) \)
51. If \( f(x) = x^3 \), then the function is:
a) One-to-one
b) Onto
c) Both one-to-one and onto
d) Neither one-to-one nor onto
Answer: c) Both one-to-one and onto
52. If \( f \) is one-to-one and \( g \) is onto, then the composition \( g \circ f \) is:
a) One-to-one
b) Onto
c) Neither one-to-one nor onto
d) Both one-to-one and onto
Answer: b) Onto
53. The function \( f(x) = x + 3 \), where \( f: \mathbb{R} \to \mathbb{R} \), is:
a) One-to-one but not onto
b) Onto but not one-to-one
c) Both one-to-one and onto
d) Neither one-to-one nor onto
Answer: c) Both one-to-one and onto
54. If \( f(x) = \log(x) \), then the function is:
a) One-to-one
b) Onto
c) Neither one-to-one nor onto
d) Both one-to-one and onto
Answer: a) One-to-one
55. The function \( f(x) = 3x - 5 \), where \( f: \mathbb{R} \to \mathbb{R} \), is:
a) One-to-one but not onto
b) Onto but not one-to-one
c) Both one-to-one and onto
d) Neither one-to-one nor onto
Answer: c) Both one-to-one and onto
56. If \( f(x) = 2x \), then the function is:
a) One-to-one but not onto
b) Onto but not one-to-one
c) Both one-to-one and onto
d) Neither one-to-one nor onto
Answer: c) Both one-to-one and onto
57. If \( f(x) = x + 1 \), then the function is:
a) One-to-one but not onto
b) Onto but not one-to-one
c) Both one-to-one and onto
d) Neither one-to-one nor onto
Answer: c) Both one-to-one and onto
58. If \( f(x) = \cos(x) \), then the function is:
a) One-to-one
b) Onto
c) Neither one-to-one nor onto
d) Both one-to-one and onto
Answer: c) Neither one-to-one nor onto
59. The function \( f(x) = x^3 - 3x + 2 \) is:
a) One-to-one but not onto
b) Onto but not one-to-one
c) Both one-to-one and onto
d) Neither one-to-one nor onto
Answer: c) Both one-to-one and onto
60. If \( f(x) = 2x - 1 \), where \( f: \mathbb{R} \to \mathbb{R} \), is:
a) One-to-one but not onto
b) Onto but not one-to-one
c) Both one-to-one and onto
d) Neither one-to-one nor onto
Answer: c) Both one-to-one and onto


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